For the function f(x)=√x-2, the average rate of change to the nearest hundredth over the interval-2 ≤ x ≤ 4 is Choose...
day

The histogram that depicts a higher standard deviation is B. Histogram B depicts the higher standard deviation, because the distribution has more dispersion.

Dispersion is a measure of how spread out the values in a data set are. Standard deviation is a specific measure of dispersion that quantifies the average amount of variation or dispersion of data points from the mean in a data set.

A histogram with a higher standard deviation will generally show a wider distribution of data, with data points spread further from the mean. We see more dispersion with Histogram B with the figures having a wide range of values so it has more standard deviation.

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The solutions of given functions are : 1. (f + g)(x) = 2x² + 3x - 2, 2. (fog)(x) = 6x² + 4, 3. (gof)(x) = 18x² - 60x + 53, 4. (f.g)(x) = 6x³ - 10x² + 9x - 15, 5. (f - g)(x) = -2x² + 3x - 8, 6. (fog)(3) = 58.

What are the functions?

We have the given functions:

f(x) = 3x - 5

g(x) = 2x² + 3

Here are the solution steps of the given functions f(x) and g(x).

1. (f + g)(x) = f(x) + g(x) = (3x - 5) + (2x² + 3) = 2x² + 3x - 2

So, (f + g)(x) = 2x² + 3x - 2.

2. (fog)(x) = f(g(x)) = f(2x² + 3) = 3(2x² + 3) - 5 = 6x² + 4

So, (fog)(x) = 6x² + 4.

3. (gof)(x) = g(f(x)) = g(3x - 5) = 2(3x - 5)² + 3 = 18x² - 60x + 53

So, (gof)(x) = 18x² - 60x + 53.

4. (f.g)(x) = f(x)g(x) = (3x - 5)(2x² + 3) = 6x³ + 9x - 10x² - 15

So, (f.g)(x) = 6x³ - 10x² + 9x - 15.

5. (f - g)(x) = f(x) - g(x) = (3x - 5) - (2x² + 3) = -2x² + 3x - 8

So, (f - g)(x) = -2x² + 3x - 8.

6. (fog)(3) = f(g(3)) = f(2(3)² + 3) = f(21) = 3(21) - 5 = 58

So, (fog)(3) = 58.

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A. result, the overall worth dropped by: 33,000

B.  r = 8.15%Round the rate of decrease to 4 decimal places.

C .If you round to the closest $50, you get value Equals $10,000

From $45,000 in 1991 to $12,000 in 2000, the car's value dropped. As a result, the overall worth dropped by:

45,000 - 12,000 = 33,000

Between 1991 and 2000, the annual rate of growth was:

r = (33,000 / 9) / 45,000 = 0.0815

Four decimal digits after rounding:

r = 0.0815

In percentage form, the appropriate response to component A is:

B.  r = 8.15%Round the rate of decrease to 4 decimal places.

C. If you round to the closest $50, you get value Equals $10,000

What is a percentage?

A ratio or figure stated as a fraction of 100 is called a percentage. It is frequently represented by the percent sign (%). 50%, for instance, is equal to 50 out of 100, or 50/100. In order to convey how big or little a number is in comparison to another, percentages are utilized. They are frequently employed in statistics, economics, and finance to convey disparities between groups or changes in values over time.

The formula below can be used to determine a car's worth in 2003 if its value continues to decline by the same percentage:

value is equal to $12,00×(1 - r)3.

Inputting r = 0.0815 results in:

worth = $9,950

If you round to the closest $50, you get:

value Equals $10,000

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Answer:

m=the slope

b=the y intercept

Step-by-step explanation:

This sign "<" could mean "less than" or "greater than"

depending on which way it is facing

in this case 4+-7 is less than 13 because

< is facing 13 and not 4+-7

meaning than 13 is a bigger number

than the sum of 4+-7 but if 4+-7 is greater than 13 then

the "<" sign would be facing 4+-7 like this: 4+-7>13

How do we know if it is true?

equation: 4+-7<13

4+-7 is -3

so -3<13.

13 is bigger than -3

which means the equation is true

What if it was false?

here is a false equation:

4>14

it is false because 4 is not a bigger number than 14

Hope this helps!

I would appreciate if you could mark me brainliest.

The answer of the given question based on the trigonometry is the nearest ten-thousandth, tan(−284°24′) is approximately equal to -0.2493.

An equivalent angle is an angle that has the same degree measure as another angle. In geometry, two angles are said to be equivalent if they have the same measure, regardless of their orientation or position in space.

Equivalent angles can be found by adding or subtracting multiples of 360° degrees from an angle. This is because an angle that has been rotated a multiple of 360° degrees has the same orientation and position as the original angle.

We can use the fact that the tangent function has period 180 degrees and that tan(x + 180°) = tan(x) for any angle x. Therefore, we can add or subtract multiples of 180° from −284°24′ to find an equivalent angle in the range of −90° to 90°.

Adding 360° to −284°24′ gives us an equivalent angle of 75°36′. Since the tangent function is positive in the first and third quadrants, we can find the value of tangent of 75°36′ or its reference angle of 14°24′.

Using a calculator, we get:

tan(14°24′) ≈ 0.2493

Therefore, to the nearest ten-thousandth, tan(−284°24′) is approximately equal to -0.2493.

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To the nearest ten-thousandth, the value of tan (-284°24') is approximately -3.7583.

We need to keep in mind that the tangent function is periodic in order to determine the value of tan(-284°24'). This means that the tangent of an angle is the same as the tangent of that angle plus or minus any multiple of 180 degrees.

So, we can add 360 degrees to -284 degrees to get an equivalent angle in the range of -180 to 180 degrees:

-284 + 360 = 76

So, we can find the tangent of -284°24' by finding the tangent of 76°24'. Using a calculator, we get:

tan(76°24') ≈ 3.7583

Therefore, To the nearest ten-thousandth, the value of tan (-284°24') is approximately -3.7583. Note that the negative sign indicates that the angle is in the third quadrant of the unit circle.

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The transfοrmatiοn f(x)↦f(-x) , the graph οf f(x) reflects it acrοss the y-axis

Optiοn B

In mathematics, a functiοn is a rule that maps each element in οne set, called the dοmain, tο exactly οne element in anοther set, called the range. A functiοn can alsο be thοught οf as a set οf οrdered pairs, where the first element in each pair belοngs tο the dοmain, and the secοnd element belοngs tο the range.

Functiοns are cοmmοnly denοted by symbοls such as f(x), g(x), οr h(x), where x represents the input variable οr independent variable, and the functiοn prοduces an οutput value οr dependent variable, which is denοted by f(x), g(x), οr h(x), respectively.

Functiοns are impοrtant in many areas οf mathematics, science, and engineering, as they prοvide a way tο describe relatiοnships between variables and make predictiοns abοut the behaviοr οf systems. They are used tο mοdel physical phenοmena, analyze data, and sοlve equatiοns, amοng οther applicatiοns.

Given :

The transfοrmatiοn f(x) -> f(-x)

Fοr example , lets take a pοint οn f(x)

Let (x,y) be a pοint οn f(x)

given f(x)- > f(-x) it means x is replaced by -x

f(x) is nοt multiplied with -1  sο y value remains the same

(x,y) be a pοint οn f(x) .

After transfοrmatiοn f(x)-> f(-x) , the pοint (x,y) ---> (-x,y)

When x is multiplied by -1 then there is a reflectiοn acrοss the y axis

Sο, the graph οf f(x) reflects it acrοss the y axis.

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Complete Question:

What does the transformation f(x)↦f(-x) do to the graph of f(x)?

a) stretches it horizontally

b) reflects it across the y-axis

c) shrinks it horizontally

d) reflects it across the x-axis

e) Submit

From expression 8 pounds x $0.25 per pound and $50 / $0.25 per pound , Earnings = $2.00 and Total pounds of cans = 200 pounds and check attachment for illustration.

An expression in mathematics is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that may be evaluated to generate a value. Expressions can be basic or complicated, containing a variety of numbers, variables, and mathematical processes.

Now,

1.  

Let the total money earned by selling aluminium cans be y and the no. of cans recycled be x then this situation can be represented by the function y = 0.25x, see attachment for illustration.

2.

If someone brings 8 pounds of cans, they will earn:

Earnings = 8 pounds x $0.25 per pound

Earnings = $2.00

3.

To earn $50, the class needs to sell:

Total pounds of cans = Total earnings / Price per pound

Total pounds of cans = $50 / $0.25 per pound

Total pounds of cans = 200 pounds

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24. The price of the motorcycle before tax was $11,500. 25. the instructor earns $28.75 per class after the raise. 26.  the sum that Kay and Shay paid, including tax, was $28.62.

An equation is a mathematical statement that asserts that two expressions are equal. Equations are used to represent relationships and constraints between variables, and are commonly used in many fields of science, engineering, and mathematics.

An equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). Each side of the equation can contain numbers, variables, mathematical operations (such as addition, subtraction, multiplication, and division), and parentheses.

The goal of solving an equation is to determine the value(s) of the variable(s) that make the equation true. This is typically done by applying mathematical operations to both sides of the equation in order to isolate the variable on one side and simplify the expression on the other side.

24. Let the price of the motorcycle before tax be represented by x. Then, we can write an equation based on the given information:

0.125x = 1437.50

Solving for x, we get:

x = 1437.50 / 0.125 = $11,500

Therefore, the price of the motorcycle before tax was $11,500.

25. The instructor now earns 115% of $50, or:

$50 x 1.15 = $57.50

Since this is the amount earned for teaching 2 classes, the amount earned per class after the raise is:

$57.50 / 2 = $28.75

Therefore, the instructor earns $28.75 per class after the raise.

26. To find how much Kay paid, we first need to calculate the tax:

0.08 x $14.50 = $1.16

So the total amount Kay paid was:

$14.50 + $1.16 = $15.66

Similarly, the tax Shay paid was:

0.08 x $12 = $0.96

So the total amount Shay paid was:

$12 + $0.96 = $12.96

Therefore, the sum that Kay and Shay paid, including tax, was:

$15.66 + $12.96 = $28.62

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Answer:

B

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] fathom = 1 yard = 3 feet

then 1 fathom = 2 × 3 feet = 6 feet

1 furlong = 660 feet , then

660 feet ÷ 6 feet = 110

there are 110 fathoms in 1 furlong

Answer: there are 210 different color-trim schemes available.

Step-by-step explanation:

To find the number of different color-trim schemes available, we need to multiply the number of choices for exterior color by the number of choices for interior color by the number of choices for trim.

Using the multiplication principle, we have:

Number of color-trim schemes = 7 * 5 * 6 = 210

Therefore, there are 210 different color-trim schemes available.

The determinant of the given matrix is bc²-cb²+ac²-ab²+a²c-a²b.

The given matrix is [tex]\left[\begin{array}{ccc}1&a&a^2\\1&b&b^2\\1&c&c^2\end{array}\right][/tex].

Determinants are considered as a scaling factor of matrices. They can be considered as functions of stretching out and the shrinking in of the matrices. Determinants take a square matrix as the input and return a single number as its output.

Here, 1(bc²-cb²)+a(c²-b²)+a²(c-b)

= bc²-cb²+ac²-ab²+a²c-a²b

Therefore, the determinant of the given matrix is bc²-cb²+ac²-ab²+a²c-a²b.

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The answer to the given question about Arithmetic Sequence and Geometric Sequence is option 2)  Arithmetic, common difference = −9

To determine if the sequence is arithmetic or geometric, we need to check if there is a constant difference between consecutive terms or a constant ratio between consecutive terms.

Let's calculate the differences between consecutive terms:

The difference between the 2nd and 1st terms is 72 - 81 = -9

The difference between the 3rd and 2nd terms is 63 - 72 = -9

The difference between the 4th and 3rd terms is 54 - 63 = -9

The differences are all the same, so the sequence is arithmetic.

Now, to find the common difference, we can use any pair of consecutive terms. Let's use the first two terms:

The difference between the 2nd and 1st terms is 72 - 81 = -9

So the common difference is -9.

Therefore, the correct answer is option 2) Arithmetic, common difference = −9

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Answer:

I'll give you a basic idea on how to do them

Pythagoras theorem

If you know two other sides of the right triangle, it's the easiest option; all you need to do is apply the Pythagorean theorem:

a² + b² = c²

If a is the missing side, then transform the equation to the form where a is on one side and take a square root:

a = √(c² - b²)

If b is unknown, then:

b = √(c² - a²)

If c is unknown, then:

c = √(a² + b²)

5.

a=5, b=7 and c=?

c=√(5^2 + 7^2)

c= √(25 + 49)

c= √74

Hope it helps:)

We can mark the points (2, 95) and (4, 145) on the grid and then draw the x-axis and y-axis to plot the points on a coordinate grid.

A linear function is a first-degree mathematical problem with one or more variables set to one and no terms with a degree higher than one. The recipe for a direct condition is y = mx + b, where m indicates the incline and b the y-catch..

given

We may use the slope-intercept form of a linear equation to graph the relationship between the number of hours worked and the fee, which is:

y = mx + b

where m is the hourly rate of $35 and b is the fixed charge of $25, y is the total amount charged, x is the number of hours worked, and m is the hourly rate.

Hence, the equation is:

y = 35x + 25

y = 35(2) + 25 = 95

y = 35(4) + 25 = 145

Hence, the line's two points are (2, 95) and (4, 145).

We can mark the points (2, 95) and (4, 145) on the grid and then draw the x-axis and y-axis to plot the points on a coordinate grid.

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Answer:129°and 51°.

Step-by-step explanation:

Following are the correct pairs given for verbal mapping statements to symbolic statements.

In mathematics, mapping, or function, is a relation between two sets, where each element of the first set (called the domain) is associated with exactly one element of the second set (called the range).

According to given information,

The verbal mapping statements can be matched to their equivalent symbolic statements as follows:

The figure is translated 4 units right and 3 units down.

Symbolic statement: (x,y) mapsto (x + 4, y - 3)

The figure is translated 4 units left and 3 units up.

Symbolic statement: (x,y) mapsto [tex](x - 4, y + 3)[/tex]

The figure is translated 3 units right and 4 units down.

Symbolic statement: (x,y) mapsto [tex](x + 3, y - 4)[/tex]

The figure is translated 3 units left and 4 units up.

Symbolic statement: (x,y) mapsto[tex](x - 3, y + 4)[/tex]

So the correct matching of the verbal mapping statements to their equivalent symbolic statements is:

The figure is translated 4 units right and 3 units down.

Symbolic statement: (x,y) mapsto [tex](x + 4, y - 3)[/tex]

The figure is translated 4 units left and 3 units up.

Symbolic statement: (x,y) mapsto[tex](x - 4, y + 3)[/tex]

The figure is translated 3 units right and 4 units down.

Symbolic statement: (x,y) mapsto [tex](x + 3, y - 4)[/tex]

The figure is translated 3 units left and 4 units up.

Symbolic statement: (x,y) mapsto [tex](x - 3, y + 4)[/tex]

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Step-by-step explanation:

When the ball hits the ground , the height = 0

  0 = 96 + 80 t - 16t^2

    Use Quadratic Formula with   a = -16      b = 80      c = 96

             to find  t=  6 seconds

Answer:

Assuming exponential growth, the number of bacteria in the Petri dish can be modeled by the equation:

N(t) = N0 * e^(kt)

where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, e is the base of the natural logarithm, k is a constant representing the growth rate, and t is the time elapsed.

We are given that there are 47 bacteria initially, so N0 = 47. After 8 hours, there are 273 bacteria, so we can use this information to solve for k:

273 = 47 * e^(k*8)

Dividing both sides by 47 and taking the natural logarithm of both sides, we get:

ln(273/47) = k*8

Simplifying this expression, we get:

k ≈ 0.53

Now we can use this value of k to find the number of bacteria after 48 hours:

N(48) = 47 * e^(0.53*48)

N(48) ≈ 1.3 * 10^12

Therefore, assuming exponential growth, there would be approximately 1.3 * 10^12 bacteria in the Petri dish after 48 hours.

The volume of the shape is 144π cubic inches and the total surface area of the shape is 114π square inches.

To find the volume and total surface area of the shape, we need to first determine the radius of the semicircle.

Since the length of the shape is 12 inches and the base is a semicircle, the diameter of the semicircle is also 12 inches. Therefore, the radius of the semicircle is half the diameter, which is 6 inches.

Now we can use the formula for the volume of a cylinder, which is:

V = (πr^2h)/2

where V is the volume, r is the radius, and h is the height.

Substituting in the values we have:

V = (π(6)^2(8))/2

V = 144π cubic inches

So the volume of the shape is 144π cubic inches.

Next, we can find the total surface area of the shape by adding the area of the semicircle base to the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is:

L = 2πrh

where L is the lateral surface area.

Substituting in the values we have:

L = 2π(6)(8)

L = 96π square inches

The formula for the area of a semicircle is:

A = (πr^2)/2

where A is the area of the semicircle.

Substituting in the values we have:

A = (π(6)^2)/2

A = 18π square inches

Adding the lateral surface area and the area of the semicircle base together, we get:

Total surface area = L + A

Total surface area = 96π + 18π

Total surface area = 114π square inches

So the total surface area of the shape is 114π square inches.

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Option D : Since the slopes of the lines representing the distance traveled by Car A and Car B over time are equal, the rates of the two cars are equal.

The graph represents the distance traveled by Car A as a function of time, and the function y = 56x represents the distance traveled by Car B as a function of time.

Since both cars are moving at a constant speed, we can compare their rates by comparing the slopes of the lines representing their distances traveled over time. The slope of a line represents the rate of change of the distance traveled over time (i.e., the speed) of the car.

The slope of the line representing Car A's distance traveled over time is equal to the rise over run, or (14 - 0)/(15 - 0) = 14/15.

The slope of the line representing Car B's distance traveled over time is equal to the rise over run, or (56 - 0)/(60 - 0) = 56/60 = 14/15.

Since both slopes are equal, the rates of the two cars are equal as well. Therefore, the correct answer is:

D) Car A and Car B are traveling at the same rate per minute.

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The graph represents the distance in miles, y, that Car A travels in x minutes. The function y = 56 x represents the distance, y, that Car B travels in x minutes. Both cars are moving at a constant rate of speed. Which BEST compares the rates of the two cars? Responses

A. The rate of Car A is 12 of a mile per minute less than the rate of Car B.

B. The rate of Car B is 16 of a mile per minute less than the rate of Car A.

C. The rate of Car B is 16 of a mile per minute greater than the rate of Car A.

D. Car A and Car B are traveling at the same rate per minute.

Answer:

To solve this problem, we need to use the Poisson distribution, which describes the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence.

Let λ be the average number of calls per minute. From the problem statement, we have λ = 2.35.

Now we need to find the probability of having at most 2 phone calls in one minute. Let X be the random variable representing the number of phone calls in one minute. Then we have:

P(X ≤ 2) = e^(-λ) * (λ^0/0!) + e^(-λ) * (λ^1/1!) + e^(-λ) * (λ^2/2!)

Substituting λ = 2.35, we get:

P(X ≤ 2) = e^(-2.35) * (2.35^0/0!) + e^(-2.35) * (2.35^1/1!) + e^(-2.35) * (2.35^2/2!)

≈ 0.422

Therefore, the probability that during one particular minute there will be at most 2 phone calls is about 0.422, or 42.2%.

Answer:

The system of equations can be represented by the matrix equation A*x = b, where A is the coefficient matrix, x is the array of unknowns, and b is the array of right-hand sides of the equations. In this case, the coefficient matrix is:

A = [[650, -1, 0],

[75, 0, 1],

[0, -120, 1]]

And the vector of right-hand sides is:

b = [650, 25080, -120]

To solve this system of equations, we need to find the value of x that satisfies the equation A*x = b. This can either be done by manual methods or by using software such as MATLAB.

Manual methods include solving for x using row-reduction techniques, such as Gaussian elimination, or using an algebraic formula for solving linear systems.

Using MATLAB, we can enter the coefficient matrix A and the vector b, create the system of equations, and solve for x using a built-in function:

A = [[650, -1, 0];

[75, 0, 1];

[0, -120, 1]];

b = [650;

25080;

-120];

x = linsolve(A,b);

format long;

disp(x);

This will output x = [0, 25.2142857143, 1.5714285714].

Alternatively, we can use an online calculator such as Wolfram|Alpha to solve the system of equations:

less

A = {{650, -1, 0}, {75, 0, 1}, {0, -120, 1}}

b = {650, 25080, -120}

Solve[A . {x, y, z} == b, {x, y, z}]

ans = {x -> 0, y -> 25.2143, z -> 1.57143}

This will output x = 0,

Therefore, the total angle measure of 4 parts of a circle divided into 8 equal parts is 180 degrees.

A circle is a two-dimensional shape that is defined as a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter. The circumference of a circle is the distance around the edge of the circle, and it is given by the formula C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. Circles are a fundamental concept in geometry and are used in many fields of mathematics, science, and engineering.

A circle has 360 degrees, and it is divided into 6 equal parts. To find the total angle measure of 1 part, we can divide 360 by 6:

360 degrees ÷ 6 = 60 degrees

Therefore, each part of the circle has an angle measure of 60 degrees.

Similarly, if the circle is divided into 5 equal parts, each part will have an angle measure of:

[tex]360 degrees / 5 = 72 degrees[/tex]

To find the total angle measure of 4 parts, we can multiply 72 degrees by 4:

[tex]72 degrees * 4 = 288 degrees[/tex]

Therefore, the total angle measure of 4 parts of a circle divided into 5 equal parts is 288 degrees.

If a circle is divided into 8 equal parts, each part will have an angle measure of:

[tex]360 degrees / 8 = 45 degrees[/tex]

To find the total angle measure of 4 parts, we can multiply 45 degrees by 4:

[tex]45 degrees / 4 = 180 degrees[/tex]

Therefore, the total angle measure of 4 parts of a circle divided into 8 equal parts is 180 degrees.

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Answer:

The answer is A) f(x) = 1 / ((x - 2)(x + 1))

Kareem borrowed $7000 from the credit union based on the given interest rate.

We may use the simple interest formula to figure out how much Kareem borrowed:

I = Prt

Where r: yearly interest rate represented as a decimal, P: borrowed principal, I: interest paid, and t: amount of time in years.

We are aware that Kareem borrowed money for 6 years at an interest rate of 6% each year. We also know that he spent $2520 on interest in total. We may determine P using the following formula:

2520 = P0.066

2520 = 0.36P

P = 7000

Kareem thus took out a $7000 loan from the credit union.

In conclusion, we utilized the simple interest formula and the provided data on the interest rate, time, and total interest paid to calculate how much money Kareem borrowed from the credit union. We discovered that he took out a loan for $7000, the principal of which accrued $2520 in interest over the course of six years at an annual rate of 6%.

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Answer:

120 - 15 = 105 pages for the chapters 105 ÷ 7 = 15 chapters Therefore, there are 15 chapters in Roger's novel. The answer is not given in the options provided, so I cannot select one.

The line of elements from the lower left corner to the upper right corner of a second order determinant is called the main diagonal or simply the diagonal. In general, the diagonal of an n x n determinant consists of the elements a11, a22, ..., ann, where ai,i denotes the element in the i-th row and i-th column of the determinant.

The monkey should be given 6.25 mL of the drug each day for five days, for a total of  31.25 mL

mg/lb is a unit of measurement that represents milligrams per pound. It is often used in the field of medicine to indicate the dosage of medication per unit of body weight.

The monkey weighs 19 lbs, and the dosage is 28mg/lb. So, the monkey needs:

19 lbs x 28 mg/lb = 532 mg

This is the total amount of the drug that the monkey needs to be given over five days.

Next, we need to find the amount of the drug in milliliters that should be given to the monkey each day.

The drug is supplied as an 85mg/mL solution, so we can calculate the amount of solution needed as:

532 mg / 85 mg/mL = 6.25 mL

Therefore, the monkey should be given 6.25 mL of the drug each day for five days, for a total of:

5 days x 6.25 mL/day = 31.25 mL

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